As far as we know, equitightness results for (REF ) have not been presented under our general assumptions before (especially in the nonlocal case), and these results are really the core of this paper. Such estimates are deduced by taking, roughly speaking, \(x\mapsto \mathbf {1}_{|x|>R}\)  as a test function in the very weak formulation of (REF ). This gives uniform tail control of the approximative solution (cf. e.g. [1]}). In examples when (REF ) conserves mass, we can summarize our equitightness results by saying that such estimates always holds in the local case, and also in the nonlocal setting when we assume that the nonlocal operator is comparable to a fractional order operator at infinity.
